0=5x^4-34x^2+45

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Solution for 0=5x^4-34x^2+45 equation: 


Simplifying
0 = 5x4 + -34x2 + 45

Reorder the terms:
0 = 45 + -34x2 + 5x4

Solving
0 = 45 + -34x2 + 5x4

Solving for variable 'x'.

Combine like terms: 0 + -45 = -45
-45 + 34x2 + -5x4 = 45 + -34x2 + 5x4 + -45 + 34x2 + -5x4

Reorder the terms:
-45 + 34x2 + -5x4 = 45 + -45 + -34x2 + 34x2 + 5x4 + -5x4

Combine like terms: 45 + -45 = 0
-45 + 34x2 + -5x4 = 0 + -34x2 + 34x2 + 5x4 + -5x4
-45 + 34x2 + -5x4 = -34x2 + 34x2 + 5x4 + -5x4

Combine like terms: -34x2 + 34x2 = 0
-45 + 34x2 + -5x4 = 0 + 5x4 + -5x4
-45 + 34x2 + -5x4 = 5x4 + -5x4

Combine like terms: 5x4 + -5x4 = 0
-45 + 34x2 + -5x4 = 0

Factor a trinomial.
(-5 + x2)(9 + -5x2) = 0


Subproblem 1
Set the factor '(-5 + x2)' equal to zero and attempt to solve:

Simplifying
-5 + x2 = 0

Solving
-5 + x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x2 = 0 + 5
x2 = 0 + 5

Combine like terms: 0 + 5 = 5
x2 = 5

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}

Subproblem 2
Set the factor '(9 + -5x2)' equal to zero and attempt to solve:

Simplifying
9 + -5x2 = 0

Solving
9 + -5x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + -5x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5x2 = 0 + -9
-5x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-5x2 = -9

Divide each side by '-5'.
x2 = 1.8

Simplifying
x2 = 1.8

Take the square root of each side:
x = {-1.341640787, 1.341640787}
Solution
x = {-2.236067978, 2.236067978, -1.341640787, 1.341640787}

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